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In my experience, we applied the 95% confidence interval to everything as a basis for making stability decisions and taking future actions. I can’t think of why any less stringent criterion would be applied to run into future dating issues (an the ire of a reviewer) and I can’t think of why tighter criterion would be beneficial, like shooting yourself in the foot. How to handle (interpret) a less than favorable statistical report would entirely depend on who/what is going to be consuming the material, then appropriate justification of that interpretation seems plausible, at least for the sake of continuing meaningful research.
